Constrained density functional theory (CDFT) is a powerful tool for the prediction of electron transfer parameters in condensed phase simulations at a reasonable computational cost. In this work we present an extension to CDFT in the popular mixed Gaussian/plane wave electronic structure package CP2K, implementing the additional force terms arising from a constraint based on Hirshfeld charge partitioning. This improves upon the existing Becke partitioning scheme, which is prone to give unphysical atomic charges. We verify this implementation for a variety of systems: electron transfer in (H₂O)₂⁺ in a vacuum, electron tunnelling between oxygen vacancy centers in solid MgO, and electron self-exchange in aqueous Ru²⁺–Ru³⁺. We find good agreement with previous plane-wave CDFT results for the same systems, but at a significantly lower computational cost, and we discuss the general reliability of condensed phase CDFT calculations.

中文翻译：

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CP2K 包中约束密度泛函理论力的实现和验证

约束密度泛函理论 (CDFT) 是一种强大的工具，用于以合理的计算成本预测凝聚相模拟中的电子转移参数。在这项工作中，我们在流行的混合高斯/平面波电子结构包 CP2K 中提出了 CDFT 的扩展，实现了由基于 Hirshfeld 电荷分配的约束产生的附加力项。这改进了现有的 Becke 分区方案，该方案容易产生非物理的原子电荷。我们在各种系统中验证了这种实现：真空中 (H ₂ O) ₂ ^{+中的电子转移、固体 MgO 中氧空位中心之间的电子隧道效应以及 Ru 2+} –Ru ³⁺水溶液中的电子自交换. 我们发现与之前相同系统的平面波 CDFT 结果非常一致，但计算成本显着降低，并且我们讨论了凝聚相 CDFT 计算的一般可靠性。